The invention is based on a damping device as generally defined hereinafter. A damping device has already been proposed in which the damper element has a feed pipe which engages a flow tube that pierces a fuel distributor line and communicates with a fuel supply line; between itself and the flow tube, the feed pipe forms a flow cross section with respect to the fuel distributor line. The disadvantage here, however, is that in order to save weight and space, the flow cross section between the feed pipe and the flow tube is kept relatively small, so that the damper element does not adequately damp both pressure fluctuations in the fuel distributor line, which are caused by pressure pulses in the injection valve, and pressure fluctuations originating in the fuel supply line, which are caused by the fuel feed pump.